H2 Maths 5.2 - Maclaurin Series: Multiplying Two Expansions

What you will learn

• Goal: Maclaurin series of e^(2 x) cos(x) up to and including the x^3 term, by multiplying truncated expansions.
• e^(2 x) = 1 + 2 x + 2 x^2 + (4/3) x^3 + ...; cos(x) truncated to 1 - x^2 / 2 (higher cosine terms would exceed x^3).
• Multiply and collect: x^0 = 1, x^1 = 2 x, x^2 = (3/2) x^2, x^3 = (1/3) x^3.